The report was filed during the Summer Olympics, which ended Sunday in Rio de Janeiro.

On August 15, Lochte said that he and three fellow swim teammates — Jack Conger, Gunnar Bentz and Jimmy Feigen — were robbed by gunmen after their taxi was pulled over by armed men posing as police. Rio police rejected this version of events and accused Lochte and the others of lying.

Video surveillance emerged showing the swimmers getting into a confrontation with armed security guards over alleged vandalism at a gas station where their taxi had stopped. The gas station manager accused the swimmers of vandalizing an area near the bathroom.

A conviction for filing a false crime report carries a maximum penalty of 18 months in prison in Brazil.

Trial in absentia?

Police want to question Lochte, 32, but the 12-time medalist left Brazil the day after the incident. "If he is summoned and does not turn up to the hearing, the trial will go ahead in the accused's absence until the final sentence is given," the Rio police statement said.

Lochte's spokeswoman told the Associated Press on Thursday that the swimmer had no comment. Lochte's lawyer, Jeffrey Ostrow, told USA Today that the swimmer had not yet heard from officials in Rio.

Lochte, who lost all four of his major sponsors Monday, picked up a new one Thursday: Pine Bros. Softish Throat Drops, which makes cough drops. The company's ad says its product is "forgiving on your throat."

After the incident at the Rio gas station, Lochte returned to the U.S.

However, as Conger and Bentz tried to leave the country three days later, Rio officials removed them from a U.S.-bound airplane and questioned them about the robbery claim. They were later allowed to leave the country. Feigen, who paid nearly $11,000 to a charity, eventually was allowed to leave as well.

Swimmer denies lying

Lochte admitted August 20 he "overexaggerated" assertions that he and the three teammates had been the victims of an armed robbery at a Rio gas station. He insisted, however, that he did not lie, but still issued an apology. "I'm sorry," he said. "Brazil doesn't deserve that."

The gas station is close to Olympic Park, where coverage of the sporting events was interspersed with reports of muggings and robberies, including incidents involving other athletes and two visiting government ministers.

Lochte's account of being held up embarrassed Rio, which had deployed 85,000 police and soldiers during the games. The news of the gas station assault also dominated news coverage of the Summer Games.

U.S. Olympic Committee CEO Scott Blackmun on Sunday said Lochte and his three teammates would face disciplinary action. Blackmun did not offer specifics but expressed frustration at their behavior.